It is unlikely that the question is about a polyhedron which is a 3-dimensional solid bounded by polygons. The minimum number of edges for a polyhedron is 6: the question appears to suggest just 4.
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No, never. Parallel lines are line that will NEVER intersect.
A transversal line cutting through parallel lines creates various angles
Each line can either intersect the edge which is common to the two planes at some point or be parallel to it. If the two lines intersect the edge, but at different points, then the lines are skew. If only one of the lines intersects the edge, then again the lines are skew. If neither of them intersect, then the two lines are parallel to the same edge and so they are parallel to one another so not skew.
the parallel lines never intersect each other but they both intersect the line they are perpendicular to
No, they can't be, if they intersect. This is because any two lines parallel to the same line are also parallel. And since they intersect, they aren't parallel.